Investigating the proton-halo structure of $^8$B via the extended THSR wave function

Abstract

Due to the proton-halo structure, the $^8$B nucleus has been attractive for many experimental and theoretical studies. In this work, we perform theoretical calculations on the ground state of $^8$B through a further extended Tohsaki–Horiuchi–Schuck–Röpke (THSR) wave function. The $^8$B nucleus is treated as an $\alpha$ + $^3$He + p system where the two clusters move inside modified containers, which are formulated in this work to describe the various modes of cluster motion. Through variational calculations, it is found that our new THSR wave functions are very efficient in describing the ground state of $^8$B, which can be accurately described by a superposition of only two basis states, namely the spindle shaped one and the elliptical one. It is of particular interest to find that the latter basis has a dominant contribution to the proton-halo structure. We further illustrate the property of the proton halo in $^8$B by calculating the radius and the electric quadrupole moment of $^8$B. The obtained result shows a large electric quadrupole moment in the ground state of $^8$B, which is in good agreement with the experimental data and other theoretical calculations. It is found that in one basis state, the large electric quadrupole moment is contributed by the polarization of the $^7$Be core, while in the other basis it is primarily due to the proton halo structure.